DerivativesIntroduction : Derivatives Introduction Professor André Farber Solvay Business School Université Libre de Bruxelles


1.Introduction: 1.Introduction Outline of this session Course outline Derivatives Forward contracts Options contracts The derivatives markets Futures contracts


Slide3: Reference: John HULL Options, Futures and Other Derivatives, Sixth edition, Pearson Prentice Hall 2006 or John HULL Options, Futures and Other Derivatives, Fifth edition, Prentice Hall 2003 Copies of my slides will be available on my website: www.ulb.ac.be/cours/solvay/farber Grades: Cases: 30% Final exam: 70%


Course outline: Course outline


Derivatives: Derivatives A derivative is an instrument whose value depends on the value of other more basic underlying variables 2 main families: Forward, Futures, Swaps Options = DERIVATIVE INSTRUMENTS value depends on some underlying asset


Forward contract: Definition: Forward contract: Definition Contract whereby parties are committed: to buy (sell) an underlying asset at some future date (maturity) at a delivery price (forward price) set in advance The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities Buying forward = "LONG" position Selling forward = "SHORT" position When contract initiated: No cash flow Obligation to transact


Forward contract: example: Forward contract: example Underlying asset: Gold Spot price: $380 / troy ounce Maturity: 6-month Size of contract: 100 troy ounces (2,835 grams) Forward price: $390 / troy ounce Profit/Loss at maturity ST ST Gain/Loss 390 390 Gain/Loss Long Short


Derivatives Markets: Derivatives Markets Exchange traded Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading Contracts are standard there is virtually no credit risk Over-the-counter (OTC) A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers Contracts can be non-standard and there is some small amount of credit risk Europe Eurex:http://www.eurexchange.com/ Liffe: http://www.liffe.com Matif : http://www.matif.fr United States Chicago Board of Trade http: //www.cbot.com


Evolution of global market: Evolution of global market


Global Market Size: Global Market Size Source: BIS Quarterly Review, June 2006 – www.bis.org


Why use derivatives?: Why use derivatives? To hedge risks To speculate (take a view on the future direction of the market) To lock in an arbitrage profit To change the nature of a liability To change the nature of an investment without incurring the costs of selling one portfolio and buying another


Forward contract: Cash flows: Forward contract: Cash flows Notations ST Price of underlying asset at maturity Ft Forward price (delivery price) set at time t

Forward contract: Locking in the result before maturity: Forward contract: Locking in the result before maturity Enter a new forward contract in opposite direction. Ex: at time t1 : long forward at forward price F1 At time t2 (

Futures contract: Definition: Futures contract: Definition Institutionalized forward contract with daily settlement of gains and losses Forward contract Buy  long sell  short Standardized Maturity, Face value of contract Traded on an organized exchange Clearing house Daily settlement of gains and losses (Marked to market) Example: Gold futures Trading unit: 100 troy ounces (2,835 grams) July 3, 2002


Futures: Daily settlement and the clearing house: Futures: Daily settlement and the clearing house In a forward contract: Buyer and seller face each other during the life of the contract Gains and losses are realized when the contract expires Credit risk BUYER  SELLER In a futures contract Gains and losses are realized daily (Marking to market) The clearinghouse garantees contract performance : steps in to take a position opposite each party BUYER  CH  SELLER


Futures: Margin requirements: Futures: Margin requirements INITIAL MARGIN : deposit to put up in a margin account MAINTENANCE MARGIN : minimum level of the margin account MARKING TO MARKET : balance in margin account adjusted daily Equivalent to writing a new futures contract every day at new futures price (Remember how to close of position on a forward) Note: timing of cash flows different + Size x (Ft+1 -Ft) -Size x (Ft+1 -Ft) LONG(buyer) SHORT(seller) Time Margin IM MM


Valuing forward contracts: Key ideas: Valuing forward contracts: Key ideas Two different ways to own a unit of the underlying asset at maturity: 1.Buy spot (SPOT PRICE: S0) and borrow => Interest and inventory costs 2. Buy forward (AT FORWARD PRICE F0) VALUATION PRINCIPLE: NO ARBITRAGE In perfect markets, no free lunch: the 2 methods should cost the same. You can think of a derivative as a mixture of its constituent underliers, much as a cake is a mixture of eggs, flour and milk in carefully specified proportions. The derivative’s model provide a recipe for the mixture, one whose ingredients’ quantity vary with time. Emanuel Derman, Market and models, Risk July 2001


Discount factors and interest rates: Discount factors and interest rates Review: Present value of Ct PV(Ct) = Ct × Discount factor With annual compounding: Discount factor = 1 / (1+r)t With continuous compounding: Discount factor = 1 / ert = e-rt


Forward contract valuation : No income on underlying asset: Forward contract valuation : No income on underlying asset Example: Gold (provides no income + no storage cost) Current spot price S0 = $300/oz Interest rate (with continuous compounding) r = 5% Time until delivery (maturity of forward contract) T = 1 Forward price F0 ? Strategy 2: buy spot and borrow Buy spot Borrow Strategy 1: buy forward


Forward price and value of forward contract: Forward price and value of forward contract Forward price: Remember: the forward price is the delivery price which sets the value of a forward contract equal to zero. Value of forward contract with delivery price K You can check that f = 0 for K = S0 e r T


Arbitrage: Arbitrage If F0 ≠ S0 e rT : arbitrage opportunity Cash and carry arbitrage if: F0 > S0 e rT Borrow S0, buy spot and sell forward at forward price F0 Reverse cash and carry arbitrage if S0 e rT > F0 Short asset, invest and buy forward at forward price F0


Arbitrage: examples: Arbitrage: examples Gold – S0 = 300, r = 5%, T = 1 S0 erT = 315. 38 If forward price = 320 Buy spot -300 +S1 Borrow +300 -315.38 Sell forward 0 +320 – S1 Total 0 + 4.62 If forward price = 310 Sell spot +300 -S1 Invest -300 +315.38 Buy forward 0 S1 – 310 Total 0 + 5.38